Earlier investigations concerning a radome have been restricted to two dimensional analysis, although there is an increasing necessity in analysis and design of practical three dimensional radomes. Recently, it has become possible to respond to this requirement by the appearance of high speed large computers. This report analyzes the radiation characteristics of an aperture antenna covered by an arbitrarily curved three dimensional radome. The aperture antenna is arbitrarily shaped, illuminated and located. It is permitted that the radome be multilayered or even inhomogeneous. The analysis is based on the method of local slab model approximation. The radiation patterns for various parameters of radomes are shown.